Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a volume of 1098.5 inches cubed. What dimensions will minimize surface area? What is the minimum surface area?

Area = s^2 + 4sh

For minimum dA/ds = 2s + 4h = 0

s = - 2h

But s^2h = 1098.5

(-2h) ^2 h = 1098.5

4h^3 = 1098.5

h^3 = 1098.5/4 = 274.625

h = cube roof of 274.625 = 6.5 inches

Thus, s^2 (6.5) = 1098.5

s^2 = 169

s = sqrt (169) = 13 inches

Therefore, to minimize the surface area, the square base should have sides of 13 inches while the height should be 6.5 inches.

Surface area = (13) ^2 + 4 (13 x 6.5) = 169 + 338 = 507 inches